In many math curricula, functions are treated as something complicated and mysterious and they don’t get introduced until some time in middle school. But in fact, the basic idea is very simple and beautiful. A few days ago I introduced the concept of a function to Katie, and again the credit for the idea goes to Moebius Noodles, this time the book. First, I tried to explain to her what a function is in words. I drew a square on a piece of paper with an ‘in’ door and an ‘out’ door. I told her that you have to decide what type of objects can go in and what comes out. I’m not sure that she fully understood and I realized that if I was to keep her attention, then examples were needed, and fast.
Since I wanted Katie to right away think that functions are really cool, my first example was: girls can go in and princesses come out. Katie was in disbelief. ‘That doesn’t exist,’ she said. I told her that functions can be real or make believe. So naturally I had to give her a ‘real life’ example next. To illustrate the importance of specifying a domain, I gave her two examples: a dishwasher and a washing machine. In both functions dirty objects go in and clean ones come out, but you wouldn’t put dishes into a washing machine or clothes into a dishwasher. She seemed to be convinced and amused.
For the next 15 minutes (which happened to coincide with bath time 🙂 ), we took turns coming up with functions. A lot of Katie’s functions involved animals. Sometimes she tried to list individually which animals can go in and which other animals they get turned into (eg, giraffe goes in, pig comes out). My three favorites from her were: 1) boys go in and boys come out (the identity function!), 2) goats go in and sheep come out, sheep go in and goats come out, and 3) one function goes in and another one comes out (the last two she didn’t come up with on that first day but at different times during the next few days).
I did not want to explicitly introduce functions of numbers right away, but to start getting her used to the idea, on some of my turns I used functions like: one animal goes in and two come out, two animals go in and three come out, etc. She seemed to particularly like this one.
Even in this short period of time, functions have already been a great source of both learning and entertainment for Katie. There were several occasions when she would be doing something and then suddenly she’d stop and say, “mommy, can I tell you about a function I came up with?” I highly recommend introducing this concept to your kids early and I would love to hear about other peoples experiences with this rich topic!